9
Applications of Multi-Degree
of Freedom Analysis
James F. Wilson
This chapter has two main purposes. The first is to apply the time domain
theory of linear dynamic analysis formulated in Chapters 7 and 8 to selected
offshore structures. For instance, response time historiés are calculated for a
jacket template platform with deterministic wave and earthquake loadings. The
second purpose is to develop in the frequency domain the response statistics for
linear structures subject to stationary, random wave excitation. This statistical
analysis represents an extension of the theory developed in Chapter 7, now
applied to multi-degree of freedom Systems.
For the illustrative problems, the mathematical models are simple: they are
two degree of freedom Systems, chosen more for the purpose of fixing the basic
ideas of dynamic analysis in the mind of the reader than for the purpose of
design. In actual practice, packaged computer codes utilizing the same essential
ideas would be employed in the final design stages where the structure would
be represented by perhaps several hundred degrees of freedom. However. back
of the envelope calculations for a structure modeled with only a few carefully
chosen dynamic coordinates hâve their place: they give the analyst a feeling
for the problem, they are economical to perform, and the results predict the
essential characteristics of motion for the same structure modeled as a higher
order System. For instance, for the simplified model of the gravity platform, the
fundamental frequency and the conclusions about the structural stability are
about the same as the results derived from the elaborate counterpart models
with many more degrees of freedom.
The emphasis of this chapter is on computational procedures and the interprétation of numerical results for structural responses. As in C hapter 8, the
linear équations representing plane structural motion in this chapter are given
by the following matrix form:
M£ + C£ + K£ = p(t)
(9.1)
223
Applications of Multi-Degree
of Freedom Analysis
James F. Wilson
This chapter has two main purposes. The first is to apply the time domain
theory of linear dynamic analysis formulated in Chapters 7 and 8 to selected
offshore structures. For instance, response time historiés are calculated for a
jacket template platform with deterministic wave and earthquake loadings. The
second purpose is to develop in the frequency domain the response statistics for
linear structures subject to stationary, random wave excitation. This statistical
analysis represents an extension of the theory developed in Chapter 7, now
applied to multi-degree of freedom Systems.
For the illustrative problems, the mathematical models are simple: they are
two degree of freedom Systems, chosen more for the purpose of fixing the basic
ideas of dynamic analysis in the mind of the reader than for the purpose of
design. In actual practice, packaged computer codes utilizing the same essential
ideas would be employed in the final design stages where the structure would
be represented by perhaps several hundred degrees of freedom. However. back
of the envelope calculations for a structure modeled with only a few carefully
chosen dynamic coordinates hâve their place: they give the analyst a feeling
for the problem, they are economical to perform, and the results predict the
essential characteristics of motion for the same structure modeled as a higher
order System. For instance, for the simplified model of the gravity platform, the
fundamental frequency and the conclusions about the structural stability are
about the same as the results derived from the elaborate counterpart models
with many more degrees of freedom.
The emphasis of this chapter is on computational procedures and the interprétation of numerical results for structural responses. As in C hapter 8, the
linear équations representing plane structural motion in this chapter are given
by the following matrix form:
M£ + C£ + K£ = p(t)
(9.1)
223